WACC: The Average Cost of a Firm's Assets

The weighted-average cost of capital (WACC) is the overall cost of capital for the firm. You can think of it as the required return on the firm's assets as a whole.

• If we are considering investing in a project that is about as risky as the overall firm, we can use the WACC as the discount rate in our NPVcalculation.

• The WACC is a function of the firm's capital structure, costs of debt and equity (and preferred stock if present), and the firm's tax rate.

The Cost of Equity

If we assume that the firm pays dividends, and these dividends (and hence the stock itself) grows at a constant rate, then we can calculate the cost of equity as:

`P_0 = \frac{D_1}{r - g} \Rightarrow r = \frac{D_1}{P_0} + g`

where r is the cost of equity, `P_0` the stock price today, `D_1` the dividend in the next period, and g the growth rate of dividends and the stock price.

The downsides of this approach are:

1. The stock must pay a constantly increasing dividend.

2. It doesn't explicitly take into account risk.

The CAPM Approach

We can also use the CAPM to estimate the cost of equity capital. Remember, the CAPM:

`R_e = R_f + \beta_e(R_m - R_f)`

where `R_e` is the cost of equity, `R_f` is the risk-free rate, `\beta_e` is the amount of systematic risk in the asset e, and the expected return on the market minus the risk-free rate `(R_m - R_f)` is the reward for bearing systematic risk.

• The benefits of this approach are that it can be applied to any stock (any capital asset) and that it explicitly takes into account risk.

• The downside is that we have to estimate two values, wheres previously we only had to estimate the dividend growth rate.

The Cost of Debt

The cost of debt is the yield required by the market on the firm's debt. If the debt is actively traded (meaning we can trust the price), then it is the bond's yield-to-maturity. If no debt is actively traded, you can infer the cost of debt from the outstanding debt's credit rating.

• Unlike equity, debt provides the firm a tax shield. This tax shield lowers the cost of debt—in essence the government is paying a portion of the interest.

• We thus adjust the cost of debt `R_d` by the amount of the tax shield, `R_d(1-\tau)` where `\tau` is the firm's tax rate.

The Cost of Preferred Stock

Since preferred stock pays a constant dividend every period forever, it is a perpetuity. Its price today is thus `P_{0, ps} = \frac{D}{R_{ps}}`.

• We can rearrange this for the cost of preferred stock, `R_{ps} = \frac{D}{P_{0, ps}}`.

• Like common stock dividends, preferred stock dividends are paid after tax, and so we do not need to adjust the preferred stock required return for taxes.

The WACC

Putting the cost of equity, debt, and preferred stock together, we get the weighted average cost of capital:

WACC `= w_eR_e + w_dR_d(1-\tau) + w_{ps}R_{ps}`

where `w_E`, `w_d`, and `w_{ps}` are the (market-value) weights of equity, debt, and preferred stock in the firm's capital structure.